Divide (x^5+7)/(x^3-1)

Problem

(x5+7)/(x3−1)

Solution

1. Set up the polynomial long division by dividing the leading term of the dividend x5 by the leading term of the divisor x3

2. Divide the first terms to get the first term of the quotient.

(x5)/(x3)=x2

3. Multiply the divisor x3−1 by the quotient term x2

x2*(x3−1)=x5−x2

4. Subtract this result from the original dividend to find the new remainder.

(x5+7)−(x5−x2)=x2+7

5. Identify the final components since the degree of the remainder x2+7 is less than the degree of the divisor x3−1

6. Write the result in the form Quotient+Remainder/Divisor

Final Answer

(x5+7)/(x3−1)=x2+(x2+7)/(x3−1)

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